How to create a Yin Yang fractal pattern using the Array modifier?

Basically, I want to create something like this:

But only using a simple Array modifier linked to an empty (rot 180, Y-pos 0.5, size 0.25), I get this:

Using another Array linked to a second empty (rot 180, Y-pos -0.5, size 0.25), I get one correct level but all other levels still lack the necessary duplications:

I made the first example image by copying the 2 array modifiers several times, alternating them. Obviously this is not a viable solution to my problem, as it keeps the asymmetric array pattern at the deeper levels while I want a perfect fractal, and I’d like to create 3D fractals that aren’t as simple and may require even more than just 2 different duplication positions.

So, in essence, I would want something like an Array modifier to apply to 2 empties at the same time, making a recursive iteration that properly duplicates the main symbol at 2 positions in each iteration so the first image is the result.

Any suggestions? Is my request even possible using Blender?

Sorry mate, I’ve been trying to recreate it using modifiers for quite some time so I guess the only option would be to make it “manually” as you already did and make ti loop in a video montage.